IDEAS home Printed from https://ideas.repec.org/a/spr/coopap/v62y2015i3p761-786.html
   My bibliography  Save this article

AAR-based decomposition algorithm for non-linear convex optimisation

Author

Listed:
  • Nima Rabiei
  • Jose Muñoz

Abstract

In this paper we present a method for decomposing a class of convex non-linear programmes which are frequently encountered in engineering plastic analysis. These problems have second-order conic memberships constraints and a single complicating variable in the objective function. The method is based on finding the distance between the feasible sets of the decomposed problems, and updating the global optimal value according to the value of this distance. The latter is found by exploiting the method of averaged alternating reflections, which is here adapted to the optimisation problem at hand. The method is specially suited for non-linear problems and as our numerical results show, its convergence is independent of the number of variables of each sub-domain. We have tested the method with an illustrative example and with problems that have more than 10,000 variables. Copyright Springer Science+Business Media New York 2015

Suggested Citation

  • Nima Rabiei & Jose Muñoz, 2015. "AAR-based decomposition algorithm for non-linear convex optimisation," Computational Optimization and Applications, Springer, vol. 62(3), pages 761-786, December.
    • Handle: RePEc:spr:coopap:v:62:y:2015:i:3:p:761-786
    DOI: 10.1007/s10589-015-9750-8
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s10589-015-9750-8
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s10589-015-9750-8?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Quoc Tran Dinh & Carlo Savorgnan & Moritz Diehl, 2013. "Combining Lagrangian decomposition and excessive gap smoothing technique for solving large-scale separable convex optimization problems," Computational Optimization and Applications, Springer, vol. 55(1), pages 75-111, May.
    2. NESTEROV, Yu., 2005. "Smooth minimization of non-smooth functions," LIDAM Reprints CORE 1819, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    3. S A Gabriel & Y Shim & A J Conejo & S de la Torre & R García-Bertrand, 2010. "A Benders decomposition method for discretely-constrained mathematical programs with equilibrium constraints," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 61(9), pages 1404-1419, September.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Jueyou Li & Zhiyou Wu & Changzhi Wu & Qiang Long & Xiangyu Wang, 2016. "An Inexact Dual Fast Gradient-Projection Method for Separable Convex Optimization with Linear Coupled Constraints," Journal of Optimization Theory and Applications, Springer, vol. 168(1), pages 153-171, January.
    2. Quoc Tran-Dinh, 2017. "Adaptive smoothing algorithms for nonsmooth composite convex minimization," Computational Optimization and Applications, Springer, vol. 66(3), pages 425-451, April.
    3. Frank E. Curtis & Arvind U. Raghunathan, 2017. "Solving nearly-separable quadratic optimization problems as nonsmooth equations," Computational Optimization and Applications, Springer, vol. 67(2), pages 317-360, June.
    4. Jueyou Li & Guo Chen & Zhaoyang Dong & Zhiyou Wu, 2016. "A fast dual proximal-gradient method for separable convex optimization with linear coupled constraints," Computational Optimization and Applications, Springer, vol. 64(3), pages 671-697, July.
    5. Murphy, Frederic & Pierru, Axel & Smeers, Yves, 2019. "Measuring the effects of price controls using mixed complementarity models," European Journal of Operational Research, Elsevier, vol. 275(2), pages 666-676.
    6. Dirk Lorenz & Marc Pfetsch & Andreas Tillmann, 2014. "An infeasible-point subgradient method using adaptive approximate projections," Computational Optimization and Applications, Springer, vol. 57(2), pages 271-306, March.
    7. Guoyin Li & Alfred Ma & Ting Pong, 2014. "Robust least square semidefinite programming with applications," Computational Optimization and Applications, Springer, vol. 58(2), pages 347-379, June.
    8. Masaru Ito, 2016. "New results on subgradient methods for strongly convex optimization problems with a unified analysis," Computational Optimization and Applications, Springer, vol. 65(1), pages 127-172, September.
    9. TAYLOR, Adrien B. & HENDRICKX, Julien M. & François GLINEUR, 2016. "Exact worst-case performance of first-order methods for composite convex optimization," LIDAM Discussion Papers CORE 2016052, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    10. Dimitris Bertsimas & Nishanth Mundru, 2021. "Sparse Convex Regression," INFORMS Journal on Computing, INFORMS, vol. 33(1), pages 262-279, January.
    11. Amir Beck & Shoham Sabach, 2015. "Weiszfeld’s Method: Old and New Results," Journal of Optimization Theory and Applications, Springer, vol. 164(1), pages 1-40, January.
    12. Donghwan Kim & Jeffrey A. Fessler, 2021. "Optimizing the Efficiency of First-Order Methods for Decreasing the Gradient of Smooth Convex Functions," Journal of Optimization Theory and Applications, Springer, vol. 188(1), pages 192-219, January.
    13. Nguyen Thai An & Nguyen Mau Nam & Xiaolong Qin, 2020. "Solving k-center problems involving sets based on optimization techniques," Journal of Global Optimization, Springer, vol. 76(1), pages 189-209, January.
    14. Manlio Gaudioso & Giovanni Giallombardo & Giovanna Miglionico, 2020. "Essentials of numerical nonsmooth optimization," 4OR, Springer, vol. 18(1), pages 1-47, March.
    15. Masoud Ahookhosh, 2019. "Accelerated first-order methods for large-scale convex optimization: nearly optimal complexity under strong convexity," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 89(3), pages 319-353, June.
    16. Sarhadi, Hassan & Tulett, David M. & Verma, Manish, 2017. "An analytical approach to the protection planning of a rail intermodal terminal network," European Journal of Operational Research, Elsevier, vol. 257(2), pages 511-525.
    17. Alexandre Belloni & Victor Chernozhukov & Lie Wang, 2013. "Pivotal estimation via square-root lasso in nonparametric regression," CeMMAP working papers CWP62/13, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    18. Chao, Shih-Kang & Härdle, Wolfgang K. & Yuan, Ming, 2021. "Factorisable Multitask Quantile Regression," Econometric Theory, Cambridge University Press, vol. 37(4), pages 794-816, August.
    19. DEVOLDER, Olivier & GLINEUR, François & NESTEROV, Yurii, 2013. "First-order methods with inexact oracle: the strongly convex case," LIDAM Discussion Papers CORE 2013016, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    20. Lingxue Zhang & Seyoung Kim, 2014. "Learning Gene Networks under SNP Perturbations Using eQTL Datasets," PLOS Computational Biology, Public Library of Science, vol. 10(2), pages 1-20, February.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:coopap:v:62:y:2015:i:3:p:761-786. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.